Quasiperfect domination in triangular lattices

Abstract

A vertex subset S of a graph G is a perfect (resp. quasiperfect) dominating set in G if each vertex v of G n S is adjacent to only one vertex (d v ε {1, 2} vertices) of S. Perfect and quasiperfect dominating sets in the regular tessellation graph of Schläfli i symbol {3, 6} and in its toroidal quotients are investigated, yielding the classi.